Evaluate Each Expression.1. $8 + 10 \cdot 3 = 38$2. $8^2 + 10 \cdot 3 = \square$

Introduction

Mathematical expressions are a fundamental part of mathematics, and evaluating them is a crucial skill that every student should possess. In this article, we will evaluate two mathematical expressions and provide a step-by-step guide on how to do it.

Expression 1: $8 + 10 \cdot 3 = 38$

Evaluating the Expression

To evaluate the expression $8 + 10 \cdot 3$, we need to follow the order of operations (PEMDAS):

1. Parentheses: There are no parentheses in the expression.
2. Exponents: There are no exponents in the expression.
3. Multiplication: We need to multiply 10 and 3.
4. Addition: We need to add 8 and the result of the multiplication.

Step-by-Step Solution

1. Multiply 10 and 3: ${ 10 \cdot 3 = 30 }$
2. Add 8 and 30: ${ 8 + 30 = 38 }$

Conclusion

The final answer to the expression $8 + 10 \cdot 3$ is 38.

Expression 2: $8^2 + 10 \cdot 3 = \square$

Evaluating the Expression

To evaluate the expression $8^2 + 10 \cdot 3$, we need to follow the order of operations (PEMDAS):

1. Parentheses: There are no parentheses in the expression.
2. Exponents: We need to evaluate the exponent 8^2.
3. Multiplication: We need to multiply 10 and 3.
4. Addition: We need to add the result of the exponent and the result of the multiplication.

Step-by-Step Solution

1. Evaluate the exponent 8^2: ${ 8^2 = 64 }$
2. Multiply 10 and 3: ${ 10 \cdot 3 = 30 }$
3. Add 64 and 30: ${ 64 + 30 = 94 }$

Conclusion

The final answer to the expression $8^2 + 10 \cdot 3$ is 94.

Understanding the Order of Operations

The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

• Parentheses: Evaluate expressions inside parentheses first.
• Exponents: Evaluate any exponential expressions next.
• Multiplication and Division: Evaluate any multiplication and division operations from left to right.
• Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Tips for Evaluating Mathematical Expressions

Here are some tips for evaluating mathematical expressions:

• Read the expression carefully: Make sure you understand what the expression is asking you to do.
• Follow the order of operations: Use the PEMDAS rules to determine which operations to perform first.
• Use parentheses: If you have multiple operations in an expression, use parentheses to group them and make it easier to evaluate.
• Check your work: Once you have evaluated the expression, check your work to make sure you got the correct answer.

Conclusion

Introduction

In our previous article, we discussed how to evaluate mathematical expressions using the order of operations (PEMDAS). In this article, we will provide a Q&A guide to help you better understand how to evaluate mathematical expressions.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

• Parentheses: Evaluate expressions inside parentheses first.
• Exponents: Evaluate any exponential expressions next.
• Multiplication and Division: Evaluate any multiplication and division operations from left to right.
• Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: Why is it important to follow the order of operations?

A: Following the order of operations is important because it ensures that we perform the operations in the correct order. If we don't follow the order of operations, we may get the wrong answer.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both operations that involve numbers, but they are performed in different ways. Multiplication involves multiplying two or more numbers together, while division involves dividing one number by another.

Q: How do I evaluate an expression with parentheses?

A: To evaluate an expression with parentheses, we need to follow the order of operations. We start by evaluating the expression inside the parentheses, and then we evaluate the rest of the expression.

Q: What is the difference between an exponent and a power?

A: An exponent and a power are both ways of expressing repeated multiplication. An exponent is a small number that is raised to a power, while a power is the result of raising a number to a power.

Q: How do I evaluate an expression with exponents?

A: To evaluate an expression with exponents, we need to follow the order of operations. We start by evaluating the exponent, and then we evaluate the rest of the expression.

Q: What is the difference between addition and subtraction?

A: Addition and subtraction are both operations that involve numbers, but they are performed in different ways. Addition involves adding two or more numbers together, while subtraction involves subtracting one number from another.

Q: How do I evaluate an expression with addition and subtraction?

A: To evaluate an expression with addition and subtraction, we need to follow the order of operations. We start by evaluating the addition and subtraction operations from left to right.

Q: What are some common mistakes to avoid when evaluating mathematical expressions?

A: Some common mistakes to avoid when evaluating mathematical expressions include:

• Not following the order of operations
• Not evaluating expressions inside parentheses first
• Not evaluating exponents before multiplication and division
• Not evaluating multiplication and division from left to right
• Not evaluating addition and subtraction from left to right

Conclusion

Evaluating mathematical expressions is an important skill that every student should possess. By following the order of operations and using the tips provided in this article, you can evaluate expressions with confidence. Remember to read the expression carefully, follow the order of operations, use parentheses, and check your work to ensure that you get the correct answer.

Additional Resources

If you need additional help with evaluating mathematical expressions, here are some additional resources that you can use:

• Math textbooks: Math textbooks are a great resource for learning how to evaluate mathematical expressions.
• Online math resources: There are many online resources available that can help you learn how to evaluate mathematical expressions, including video tutorials and practice problems.
• Math tutors: If you need one-on-one help with evaluating mathematical expressions, consider hiring a math tutor.

Practice Problems

Here are some practice problems that you can use to practice evaluating mathematical expressions:

• Evaluate the expression: 2 + 3 × 4
• Evaluate the expression: 5 - 2 × 3
• Evaluate the expression: 7 + 2^3
• Evaluate the expression: 9 - 3^2

Answer Key

Here are the answers to the practice problems:

• 2 + 3 × 4 = 14
• 5 - 2 × 3 = 1
• 7 + 2^3 = 15
• 9 - 3^2 = 0